Billionaires have a January dilemma on their hands: Attend President-elect Trump’s inauguration on Jan. 20 or stay for the third and final day of the annual World Economic Forum in the Swiss Alps village of Davos.

In other worlds, to ski or to schmooze.

It is the first time in recent memory that the WEF and the inauguration of a US president conflict.

Many big-name US invitees are skipping the snowy get-together this year, sources said, because there is so much happening back home.

Still, the WEF isn’t hurting. There has been a host of reports suggesting WEF officials were thinking about trucking in shipping containers to serve as emergency housing for staff — to free up luxe hotels in favor of the 11,000 guests.

Fon Mathuros, a WEF spokesman, said the group was not out to mess with Washington by scheduling its gabfest to run through Jan. 20. “The dates for our annual meetings have been fixed [for] at least 5 years,” he said.